Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

Vaibhav can do a piece of work in 60 days. He works for 15 days and then Sandeep alone finishes the remaining work in 30 days. In how many days will Vaibhav and Sandeep working together finish the work?

  1. 20 days

  2. 24 days

  3. 18 days

  4. 22 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vaibhav's work in 15 days = 15/60 = 1/4. Remaining work = 3/4. Sandeep does 3/4 work in 30 days, so Sandeep's rate = (3/4)/30 = 1/40 per day. Combined rate = 1/60 + 1/40 = (2+3)/120 = 5/120 = 1/24. Together they finish in 24 days.

Multiple choice

Humans and robots can both perform a job but with different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

  1. 32

  2. 36

  3. 40

  4. 45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let H and R be the daily work of a human and a robot. 15H + 5R = 1/30. 5H + 15R = 1/60. Multiply first by 3: 45H + 15R = 3/30 = 1/10. Subtract second: 40H = 1/10 - 1/60 = 5/60 = 1/12. H = 1/480. 15H = 15/480 = 1/32. Time = 32 days.

Multiple choice

Directions: Solve the following question and mark the best possible option. Amal can complete ajob in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs. 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamals share, in rupees, is

  1. 100

  2. 200

  3. 300

  4. 400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Amal's rate is 1/10 per day, Bimal's is 1/8 per day, and their combined rate with Kamal is 1/4 per day. Kamal's daily rate is 1/4 - (1/10 + 1/8) = 1/4 - 9/40 = 1/40. Since they work for 4 days, the total work done by Kamal is 4 * (1/40) = 1/10 of the total job, so his share is 1/10 of 1000, which is 100.

Multiple choice

It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

  1. 3 days

  2. 13 days

  3. 10 days

  4. 5 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work = 52 men * 10 days = 520 man-days. With 12 men leaving, 40 men remain. Days required = 520 / 40 = 13 days. The increase over the original 10 days is 13 - 10 = 3 days.

Multiple choice

A works twice as fast as B and B works twice as fast as C. All three working together can finish a task in 4 days with the help of D. If D alone can finish the same task in 16 days, then in how many days will A alone finish 75% of the same task?

  1. 8

  2. 7

  3. 9

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C = x, B = 2x, A = 4x. Combined rate = 7x. (7x + 1/16) * 4 = 1. 28x + 1/4 = 1 => 28x = 3/4 => x = 3/112. A's rate = 4x = 12/112 = 3/28. Time for 75% work = (0.75) / (3/28) = (3/4) * (28/3) = 7 days.

Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. 7 men and 4 women can complete a piece of job in 5 days. Also, 7 boy and 3 women can complete the same job in 7 days. Quantity I: The time taken to complete the piece of job by one man, one woman and one boy. Quantity II: 21 days.

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

P, Q and R take (x - 28) days, (x - 18) days and (x - 8) days respectively to complete a job. The three work in a rotation to complete the job with only 1 person working on a day. Who should start the job so that the job is completed in the least possible time?

  1. P

  2. Q

  3. R

  4. Any one of the three

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P, Q, R take x-28, x-18, x-8 days. Their rates are 1/(x-28), 1/(x-18), 1/(x-8). To finish in the least time, the person with the highest rate (shortest time) should start. Since x-28 < x-18 < x-8, P is the fastest.

Multiple choice

A, B and C can complete a work in 20 days working together. A and B together are 50% more efficient than C and A & C together are 100% more efficient than B. Then in how many days A alone can complete the work?

  1. 85 days

  2. 80 days

  3. 75 days

  4. 65 days

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let efficiencies be A, B, C. (A+B+C) = 1/20. (A+B) = 1.5C. (A+C) = 2B. Solving the system: A+B+C = 1.5C + C = 2.5C = 1/20 => C = 1/50. A+C = 2B => A+1/50 = 2B. A+B+1/50 = 1/20 => A+B = 3/100. Solving gives A = 1/75. A takes 75 days.